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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 434 · 40 questions
TalentJR

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

NameDateTime takenScore ___ / 40
  1. 1.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 187 (b) 196 (c) 188 (d) 178
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 83? (a) 18 (b) 19 (c) 20 (d) 8
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 21 (b) 20 (c) 19 (d) 9
  4. 4.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 63 (c) 180 (d) 20
  5. 5.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 223 (c) 213 (d) 220
  6. 6.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 12 (b) 39 (c) 108 (d) 36
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 8 (b) 5 (c) 7 (d) 6
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 17 (b) 7 (c) 19 (d) 18
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 3 (b) 5 (c) 6 (d) 4
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 55? (a) 3 (b) 4 (c) 6 (d) 5
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 45? (a) 3 (b) 5 (c) 2 (d) 4
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 4 (b) 2 (c) 5 (d) 3
  13. 13.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 309 (b) 318 (c) 319 (d) 284
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 3 (b) 5 (c) 4 (d) 2
  15. 15.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  16. 16.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 2 (b) 3 (c) 5 (d) 4
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 80? (a) 17 (b) 8 (c) 19 (d) 18
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 35? (a) 3 (b) 1 (c) 4 (d) 2
  20. 20.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 14 (c) 42 (d) 126
  21. 21.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 45 (c) 5 (d) 15
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 84? (a) 8 (b) 17 (c) 19 (d) 18
  23. 23.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  24. 24.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 89 (c) 98 (d) 80
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 4 (b) 3 (c) 2 (d) 5
  26. 26.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 57? (a) 15 (b) 17 (c) 16 (d) 5
  28. 28.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 17 (d) 3
  29. 29.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 15 (b) 48 (c) 135 (d) 45
  30. 30.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 54 (c) 162 (d) 18
  31. 31.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 50 (c) 42 (d) 41
  32. 32.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 59 (c) 60 (d) 50
  33. 33.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 66 (c) 75 (d) 76
  34. 34.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 4 (d) 15
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 10 (b) 11 (c) 9 (d) 8
  36. 36.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 321 (c) 214 (d) 213
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 2 (b) 1 (c) 3 (d) 4
  38. 38.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 176 (c) 175 (d) 166
  39. 39.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 6 (c) 21 (d) 54
  40. 40.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 343 (b) 342 (c) 333 (d) 300

Answer key

  1. 187
  2. 19
  3. 20
  4. 60
  5. 222
  6. 36
  7. 7
  8. 18
  9. 5
  10. 5
  11. 4
  12. 4
  13. 318
  14. 4
  15. 4
  16. 9
  17. 4
  18. 18
  19. 3
  20. 42
  21. 15
  22. 18
  23. 6
  24. 89
  25. 4
  26. 2
  27. 16
  28. 3
  29. 45
  30. 54
  31. 41
  32. 59
  33. 75
  34. 5
  35. 10
  36. 213
  37. 3
  38. 175
  39. 18
  40. 342

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